Sharkey Ward's "opinions" on what happened in the Falklands are largely discredited by other Harrier pilots who were there too. The "natural competition" between RAF and RN pilots was more than a little exaggerated in Ward's case - it seems by the majority of post combat reports by both other RN and RAF pilots.
And without being partisan (I'm ex RAF, but not a pilot, and was already a civvy at the time of the Falklands war), the crews for the Harriers were drawn just as much from the RAF as from the RN - that MUST be so because the number of qualified RN pilots was MUCH smaller than the number of RAF pilots (unfortunately), and in addition, the majority of RN pilots were helicopter pilots at that time. Though the majority of RAF Harrier pilots were flying in the ground attack role, several RAF also flew the RN's Harrier "fighter" variant.
In addition, "the" Vulcan raid on the Falklands was more that a one off, there were several, although it was the first, Black Buck One which cratered the Falklands runway.
As an example of Ward's senseless partisanship RN v RAF, he claimed that Black Buck One resulted in only one 1,000 lb bomb (out of total 21) actually on the runway, (which is true). But his argument that this was a waste of time/resources completely ignores the fact that the result of that one bomb resulted in the Argentinians being unable to use the runway for their fast jets (A4s, Mirages, and Canberras) leaving only C130 Hercules and Pucaras able to land and take of there - they COULD have repaired the runway but never did, which was good for the end result as far as UK was concerned.
In addition, that one "successful" Vulcan Black Buck raid also involved I think 19 RAF Victor in flight refuelling tankers to get that one Vulcan there and back (to Ascension Island). And as said there were about 8 Vulcan Black Buck raids on the Falklands.
And almost finally re your "the RAF did get briefly involved" (what rot!), the "air bridge" between the UK and Ascension Island was performed solely by the RAF, using Hercules, VC-10s, and Tristars. That started before the naval task force arrived off the Falklands (in fact the RAF performed some drops of vital equipment AND personnel while the fleet was at sea on their way) and continued throughout the whole campaign plus long after the end.
And now finally, after the Argentinians surrendered, it was the RAF and Army who got the airfield back into full use again and the RAF which provided the F4 Phantoms to station a standing Combat Air Patrol and interception jet fighter force on the airfield.
Unlike "Sharkey" Ward, I and many of my ex-RAF colleagues have/had the greatest respect for out RN colleagues (even though we all pulled each others' legs on more than on occasion) but as said above, to say that the RAF played only a limited role is complete nonsense and re-quotes a largely discredited version of the conflict - discredited by the majority of those who were there. I wasn't thank goodness.
But by all means continue to enjoy Ward's version of "Biggles Wins Again" (it's a good book) but don't quote it as being anything like true - it isn't - or more accurately said, it is hopelessly one-sided.